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§31. The schematism of the pure concepts

chalkboard. These two things [the five dots and the two numeric signs]122 have absolutely nothing to do with each other. The most they have in common is that both have been written with chalk on the chalkboard. But these five dots certainly do have to do with “5,” that is, with the concept that this numeric sign means. That is: these five dots are able to be counted by means of the concept “five,” and when it comes to their “how-many,” they can be determined as this many thanks to the concept “five.” So, even though these five dots, taken in their pure thing-ness, have nothing to do with the [368] concept “five,” they still do have a specific connection with the number “five” insofar as they are what-gets-counted, or what-can-be-counted, with this number.

In a certain sense, these five dots have a closer relation to the concept “five” than they do when I (as we say) “enumerate” them as “table, chair, pen, book, ashtray.” Those things are also “five” as long as I abstract from their content and see each of them as just a “onesomething,” and then see each “one-something” as determinable in another possible “one” and as addable as this set of “ones.” In a certain sense, the five dots have a closer relation to the number insofar as (1) they are not different in their content the way the five objects I mentioned are and (2) the viewpoint of “how many?” is more immediate. In addition, (3) this spatial ordering of the five dots likewise demonstrates the series-character of a numeric manifold, much more than when I depict the five dots in the form of ⋅..⋅—although on the other hand one can and must say that, when it comes to indicating numbers in the natural and pre-theoretical order, very specific constellations (and not just dots-in-a-row) are employed.

Therefore, on the basis of their more limited content and greater lack of differentiation, these five dots somehow have a closer relation to the concept “five.” But what we saw earlier regarding the sensible depiction of geometric figures holds here as well, only in a different form. These five dots are just as essentially different from the concept “five” as any five specific objects, regardless of their content, that one might choose. Therefore we have to keep separate:



122. [The referent of the German “diese beiden Dinge” is ambiguous. It could refer to the two numeric signs—the 5 and the V—that Heidegger has just written on the chalkboard. It is also possible that “these two things” refers, on the one hand, to the five dots, and on the other hand, to the 5 and V taken together. In that case, Heidegger would have earlier drawn the five dots with chalk on the chalkboard. And it would seem he did. Twice in this paragraph he speaks of “these five dots,” thereby giving the impression that they too, like the 5 and the V, were up on the chalkboard.]


Martin Heidegger (GA 21) Logic : the question of truth

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